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• Preface
• Introduction
• Linear Relations in Hilbert Spaces
• Elementary facts about linear relations
• Spectra, resolvent sets, and points of regular type
• Adjoint relations
• Symmetric relations
• Self-adjoint relations
• Maximal dissipative and accumulative relations
• Intermediate extensions and von Neumann's formulas
• Adjoint relations and indefinite inner products
• Convergence of sequences of relations
• Parametric representations for relations
• Resolvent operators with respect to a bounded operator
• Nevanlinna families and their representations
• Boundary Triplets and Weyl Functions
• Boundary triplets
• Boundary value problems
• Associated ...-fields and Weyl functions
• Existence and construction of boundary triplets
• Transformations of boundary triplets
• Kreĭn's formula for intermediate extensions
• Kreĭn's formula for exit space extensions
• Perturbation problems
• Spectra, Simple Operators, and Weyl Functions
• Analytic descriptions of minimal supports of Borel measures
• Growth points of finite Borel measures
• Spectra of self-adjoint relations
• Simple symmetric operators
• Eigenvalues and eigenspaces
• Spectra and local minimality
• Limit properties of Weyl functions
• Spectra and local minimality for self-adjoint extensions
• Operator Models for Nevanlinna Functions
• Reproducing kernel Hilbert spaces
• Realization of uniformly strict Nevanlinna functions
• Realization of scalar Nevanlinna functions via L²-space models
• Realization of Nevanlinna pairs and generalized resolvents
• Kreĭn's formula for exit space extensions
• Orthogonal coupling of boundary triplets
• Boundary Triplets and Boundary Pairs for Semibounded Relations
• Closed semibounded forms and their representations
• Ordering and monotonicity
• Friedrichs extensions of semibounded relations
• Semibounded self-adjoint extensions and their lower bounds
• Boundary triplets for semibounded relations
• Boundary pairs and boundary triplets
• Sturm-Liouville Operators
• Sturm-Liouville differential expressions
• Maximal and minimal Sturm-Liouville differential operators
• Regular and limit-circle endpoints
• The case of one limit-point endpoint
• The case of two limit-point endpoints and interface conditions
• Exit space extensions
• Weyl functions and subordinate solutions
• Semibounded Sturm-Liouville expressions in the regular case
• Closed semibounded forms for Sturm-Liouville equations
• Principal and nonprincipal solutions of Sturm-Liouville equations
• Semibounded Sturm-Liouville operators and the limit-circle case
• Semibounded Sturm-Liouville operators and the limit-point case
• Integrable potentials
• Canonical Systems of Differential Equations
• Classes of integrable functions
• Canonical systems of differential equations
• Regular and quasiregular endpoints
• Square-integrability of solutions of real canonical systems
• Definite canonical systems
• Maximal and minimal relations for canonical systems
• Boundary triplets for the limit-circle case
• Boundary triplets for the limit-point case
• Weyl functions and subordinate solutions
• Special classes of canonical systems
• Schrodinger Operators on Bounded Domains
• Rigged Hilbert spaces
• Sobolev spaces, C²-domains, and trace operators
• Trace maps for the maximal Schrödinger operator
• A boundary triplet for the maximal Schrödinger operator
• Semibounded Schrödinger operators
• Coupling of Schrödinger operators
• Bounded Lipschitz domains
• Integral Representations of Nevanlinna Functions
• Borel transforms and their Stieltjes inversion
• Scalar Nevanlinna functions
• Operator-valued integrals
• Operator-valued Nevanlinna functions
• Kac functions
• Stieltjes and inverse Stieltjes functions
• Self-adjoint Operators and Fourier Transforms
• The scalar case
• The vector case
• Sums of Closed Subspaces in Hilbert Spaces
• Factorization of Bounded Linear Operators
• Notes
• Bibliography
• List of Symbols
• Index

This open access book presents a comprehensive survey of modern operator techniques for boundary value problems and spectral theory, employing abstract boundary mappings and Weyl functions. It includes self-contained treatments of the extension theory of symmetric operators and relations, spectral characterizations of selfadjoint operators in terms of the analytic properties of Weyl functions, form methods for semibounded operators, and functional analytic models for reproducing kernel Hilbert spaces. Further, it illustrates these abstract methods for various applications, including Sturm-Liouville operators, canonical systems of differential equations, and multidimensional Schroedinger operators, where the abstract Weyl function appears as either the classical Titchmarsh-Weyl coefficient or the Dirichlet-to-Neumann map. The book is a valuable reference text for researchers in the areas of differential equations, functional analysis, mathematical physics, and system theory. Moreover, thanks to its detailed exposition of the theory, it is also accessible and useful for advanced students and researchers in other branches of natural sciences and engineering.
(source: Nielsen Book Data)

• Preliminaries
• Proof of proposition 1.1
• Calculus of brackets for group presentation (1.2)
• Proofs of theorem 1.2 and corollary 1.3
• Calculus of brackets for group presentation (1.4)
• Proof of theorem 1.4
• Minimizing diagrams over (1.2) and proofs of theorem 1.5 and corollary 1.6
• Construction of minimal diagrams over (1.4) and proof of theorem 1.7
• Polygonal curves in the plane and proofs of theorems 1.8, 1.9 and corollary 1.10.

The author introduces and studies the bounded word problem and the precise word problem for groups given by means of generators and defining relations. For example, for every finitely presented group, the bounded word problem is in NP, i.e., it can be solved in nondeterministic polynomial time, and the precise word problem is in PSPACE, i.e., it can be solved in polynomial space. The main technical result of the paper states that, for certain finite presentations of groups, which include the Baumslag-Solitar one-relator groups and free products of cyclic groups, the bounded word problem and the precise word problem can be solved in polylogarithmic space. As consequences of developed techniques that can be described as calculus of brackets, the author obtains polylogarithmic space bounds for the computational complexity of the diagram problem for free groups, for the width problem for elements of free groups, and for computation of the area defined by polygonal singular closed curves in the plane. The author also obtains polynomial time bounds for these problems.
(source: Nielsen Book Data)

For introductory biology course for science majors Focus. Practice. Engage. Built unit-by-unit, Campbell Biology in Focus achieves a balance between breadth and depth of concepts to move students away from memorization. Streamlined content enables students to prioritize essential biology content, concepts, and scientific skills that are needed to develop conceptual understanding and an ability to apply their knowledge in future courses. Every unit takes an approach to streamlining the material to best fit the needs of instructors and students, based on reviews of over 1,000 syllabi from across the country, surveys, curriculum initiatives, reviews, discussions with hundreds of biology professors, and the Vision and Change in Undergraduate Biology Education report. Maintaining the Campbell hallmark standards of accuracy, clarity, and pedagogical innovation, the 3rd Edition builds on this foundation to help students make connections across chapters, interpret real data, and synthesize their knowledge. The new edition integrates new, key scientific findings throughout and offers more than 450 videos and animations in Mastering Biology and embedded in the new Pearson eText to help students actively learn, retain tough course concepts, and successfully engage with their studies and assessments. Also available with Mastering Biology By combining trusted author content with digital tools and a flexible platform, Mastering personalizes the learning experience and improves results for each student. Built for, and directly tied to the text, Mastering Biology enables an extension of learning allowing students a platform to practice, learn, and apply outside of the classroom. Note: You are purchasing a standalone product; Mastering Biology does not come packaged with this content. Students, if interested in purchasing this title with Mastering Biology ask your instructor for the correct package ISBN and Course ID. Instructors, contact your Pearson representative for more information. If you would like to purchase both the physical text and Mastering Biology search for: 0134875044 / 9780134875040 Campbell Biology in Focus Plus Mastering Biology with Pearson eText -- Access Card Package Package consists of: 0134710673 / 9780134710679 Campbell Biology in Focus 013487451X / 9780134874517 Mastering Biology with Pearson eText -- ValuePack Access Card -- for Campbell Biology in Focus.
(source: Nielsen Book Data)

"Cell death plays a critical role in development, normal physiology, and many diseases, including cancer. This new edition on the subject provides a state-of-the-art summary of our understanding of the signaling mechanisms that regulate cell survival and cell death, along with the molecular mechanisms underlying the various different death processes seen in cells"-- Provided by publisher

• 1. Reductive groups and Steinberg maps--
• 2. Lusztig's classification of irreducible characters--
• 3. Harish-Chandra theories--
• 4. Unipotent characters-- Appendix. Further reading and open questions-- References-- Index.
• (source: Nielsen Book Data)

Through the fundamental work of Deligne and Lusztig in the 1970s, further developed mainly by Lusztig, the character theory of reductive groups over finite fields has grown into a rich and vast area of mathematics. It incorporates tools and methods from algebraic geometry, topology, combinatorics and computer algebra, and has since evolved substantially. With this book, the authors meet the need for a contemporary treatment, complementing in core areas the well-established books of Carter and Digne-Michel. Focusing on applications in finite group theory, the authors gather previously scattered results and allow the reader to get to grips with the large body of literature available on the subject, covering topics such as regular embeddings, the Jordan decomposition of characters, d-Harish-Chandra theory and Lusztig induction for unipotent characters. Requiring only a modest background in algebraic geometry, this useful reference is suitable for beginning graduate students as well as researchers.
(source: Nielsen Book Data)

For courses in chemistry. Actively engage students to become expert problem solvers and critical thinkers Nivaldo Tro's Chemistry: A Molecular Approach presents chemistry visually through multi-level images-macroscopic, molecular, and symbolic representations-to help students see the connections between the world they see around them, the atoms and molecules that compose the world, and the formulas they write down on paper. Interactive, digital versions of select worked examples instruct students how to break down problems using Tro's unique "Sort, Strategize, Solve, and Check" technique and then complete a step in the example. To build conceptual understanding, Dr. Tro employs an active learning approach through interactive media that requires students to pause during videos to ensure they understand before continuing. The 5th Edition pairs digital, pedagogical innovation with insights from learning design and educational research to create an active, integrated, and easy-to-use framework. The new edition introduces a fully integrated book and media package that streamlines course set up, actively engages students in becoming expert problem solvers, and makes it possible for professors to teach the general chemistry course easily and effectively. Also available with Mastering Chemistry By combining trusted author content with digital tools and a flexible platform, Mastering personalizes the learning experience and improves results for each student.The fully integrated and complete media package allows instructors to engage students before they come to class, hold them accountable for learning during class, and then confirm that learning after class. Note: You are purchasing a standalone product; Mastering Chemistry does not come packaged with this content. Students, if interested in purchasing this title with Mastering Chemistry, ask your instructor for the correct package ISBN and Course ID. Instructors, contact your Pearson representative for more information. If you would like to purchase both the physical text and Mastering Chemistry, search for: 0134988809 / 9780134988801 Chemistry: A Molecular Approach Plus Mastering Chemistry with Pearson eText -- Access Card Package Package consists of: 0134874374 / 9780134874371 Chemistry: A Molecular Approach 013498854X / 9780134988542 Mastering Chemistry with Pearson eText -- ValuePack Access Card -- for Chemistry: A Molecular Approach.
(source: Nielsen Book Data)

• Part I. The Interrelationships of Organisms:
• 1. What this book is about--
• 2. Classification-- Part II. Systematics: Exposing Myths:
• 3. Relationship diagrams--
• 4. Essentialism and typology--
• 5. Monothetic and polythetic taxa--
• 6. Non-taxa or the absence of -phyly: paraphyly and aphyly-- Part III. The Cladistic Programme:
• 7. Parameters of classification: ordo ab chao-- Part IV. How to Study Classification:
• 8. Modern artificial methods and raw data--
• 9. How to study classification: consensus techniques and general classifications--
• 10. How to study classification - 'total evidence' vs 'consensus', character congruence vs taxonomic congruence, simultaneous analysis vs partitioned data--
• 11. How to study classification: natural methods I - consensus revisited--
• 12. How to study classification: natural methods II - beyond method, the philosophy of three-item analysis-- Part V. Beyond Classification:
• 13. Beyond classification: how to study phylogeny--
• 14. The separation of classification and phylogenetics--
• 15. Further myths and misunderstandings.
• (source: Nielsen Book Data)

This new edition of a foundational text presents a contemporary review of cladistics, as applied to biological classification. It provides a comprehensive account of the past fifty years of discussion on the relationship between classification, phylogeny and evolution. It covers cladistics in the era of molecular data, detailing new advances and ideas that have emerged over the last twenty-five years. Written in an accessible style by internationally renowned authors in the field, readers are straightforwardly guided through fundamental principles and terminology. Simple worked examples and easy-to-understand diagrams also help readers navigate complex problems that have perplexed scientists for centuries. This practical guide is an essential addition for advanced undergraduates, postgraduates and researchers in taxonomy, systematics, comparative biology, evolutionary biology and molecular biology.
(source: Nielsen Book Data)

• Preface and Acknowledgments
• Part 1: Introduction 1Socio-Cognitive Abilities in Animals as the Object of Science-and What Has Been Neglected Thus Far 2Questions and Objectives of the Book
• Part 2: Socio-Cognitive Abilities in Animals 3The Concept of Cognition and the Concept of Consciousness 4Culture in Animals? 4.1Animal Tool Use and Tool Production: a Widespread Phenomenon 4.2Theoretical Considerations 4.3Culture in Chimpanzees 4.4Culture in Orangutans, Gorillas, and Dolphins 4.5Culture in New Caledonian Crows 4.6Can We Speak Meaningfully of "Culture" in Animals? 5Language in Animals? 5.1Language: the Ultimate Differentia Specifica? 5.2Concept Possession as Prerequisite for Language 5.3Functional and Intentional Aspects of Natural Animal Communication 5.4Propositional Representations and Basic Grammar: First Notes from Language-Teaching Experiments 5.5Can We Speak Meaningfully of "Language" in Animals? 6Theory of Mind in Animals? 6.1Theory of Mind as Everyday Psychology 6.2Theory of Mind Research in Children 6.3Theory of Mind in Animals: What Do Animals Know about Perceptual States and False Beliefs? 6.4Can We Speak Meaningfully of "Theory of Mind" in Animals? 7Summary and Transition
• Part 3: The Relevance of Socio-Cognitive Abilities in Animals for Animal Ethics and Animal Welfare 8Kinship and Responsibility: the Moral Status of Animals 8.1Introduction to Basic Concepts in Animal Ethics 8.2Basic Positions in Animal Ethics 8.3"Classical" Arguments in Animal Ethics and Animal Welfare 8.4A "New" Argument: Personhood Rights for Animals 8.5Problems and Limits of Personhood Rights 8.6Opportunities for Personhood Rights: "Cognitive Relatives" as Ambassadors of Species Protection? 9Kinship and Responsibility: the Discrepancy between Ethical Demands and the Status Quo 9.1Case Study: How We Treat Great Apes 9.2Case Study: How We Treat Dolphins 10Summary
• Part 4: Discussion 11Cognitive Kinship and the Concept of an Evolutionary Self 11.1Animals as Strangers and Kin at the Same Time 11.2On the Way to a Nature Deficit of a Special Kind 12A Comparison of Arguments 12.1Animal Welfare Arguments vs. Species Conservation Arguments 12.2Utilitarian Pathocentrism vs. Personhood Rights 12.3Rights that Go Beyond the Weighing of Goods 12.4Criteria that Go Beyond the Ability to Consciously Suffer 12.5Painless Killing and Production of Insensitive Animals 13Possibilities of Modifying Personhood Rights for Animals 13.1Toward a Consistently Gradual Understanding 13.2Personhood Status Despite Being a "Gradual" Person? 13.3Species-Specific Inalienable Rights? 13.4Differentiation between Clear and Less Clear Cases? 14Alternative: Turn the Focus Back to the Suffering of Animals? 14.1The Relationship between the Ability to Suffer and Socio-Cognitive Abilities 14.2Socio-Cognitive Abilities, Animal Welfare, and Species Conservation 14.3Indicators of Well-being in Captivity 14.4Enrichment as Occupational Therapy 14.5Cognition-Motivation-Frustration: the Need to Gain Information and Engage in Exploratory Behavior 14.6The Difficulty of Assessing Behavioral Disorders, Using Stereotypies as an Example 14.7The Effects of Enrichment 14.8Enrichment in Captivity as an Ethical Necessity 15Final Evaluation of Personhood Rights for Animals Acknowledgements Bibliography Index.
• (source: Nielsen Book Data)

In Cognitive Kin, Moral Strangers?, Judith Benz-Schwarzburg reveals the scope and relevance of cognitive kinship between humans and non-human animals. She presents a wide range of empirical studies on culture, language and theory of mind in animals and then leads us to ask why such complex socio-cognitive abilities in animals matter. Her focus is on ethical theory as well as on the practical ways in which we use animals. Are great apes maybe better described as non-human persons? Should we really use dolphins as entertainers or therapists? Benz-Schwarzburg demonstrates how much we know already about animals' capabilities and needs and how this knowledge should inform the ways in which we treat animals in captivity and in the wild.
(source: Nielsen Book Data)

• Introduction--
• 1. Geometry of surfaces in R^3--
• 2. Vector fields--
• 3. Sub-Riemannian structures--
• 4. Pontryagin extremals: characterization and local minimality--
• 5. First integrals and integrable systems--
• 6. Chronological calculus--
• 7. Lie groups and left-invariant sub-Riemannian structures--
• 8. Endpoint map and exponential map--
• 9. 2D almost-Riemannian structures--
• 10. Nonholonomic tangent space--
• 11. Regularity of the sub-Riemannian distance--
• 12. Abnormal extremals and second variation--
• 13. Some model spaces--
• 14. Curves in the Lagrange Grassmannian--
• 15. Jacobi curves--
• 16. Riemannian curvature--
• 17. Curvature in 3D contact sub-Riemannian geometry--
• 18. Integrability of the sub-Riemannian geodesic flow on 3D Lie groups--
• 19. Asymptotic expansion of the 3D contact exponential map--
• 20. Volumes in sub-Riemannian geometry--
• 21. The sub-Riemannian heat equation-- Appendix. Geometry of parametrized curves in Lagrangian Grassmannians with Igor Zelenko-- References-- Index.
• (source: Nielsen Book Data)

Sub-Riemannian geometry is the geometry of a world with nonholonomic constraints. In such a world, one can move, send and receive information only in certain admissible directions but eventually can reach every position from any other. In the last two decades sub-Riemannian geometry has emerged as an independent research domain impacting on several areas of pure and applied mathematics, with applications to many areas such as quantum control, Hamiltonian dynamics, robotics and Lie theory. This comprehensive introduction proceeds from classical topics to cutting-edge theory and applications, assuming only standard knowledge of calculus, linear algebra and differential equations. The book may serve as a basis for an introductory course in Riemannian geometry or an advanced course in sub-Riemannian geometry, covering elements of Hamiltonian dynamics, integrable systems and Lie theory. It will also be a valuable reference source for researchers in various disciplines.
(source: Nielsen Book Data)

• Carnot groups
• Carnot groups of Iwasawa type and conformal mappings
• Metric and geometric properties of conformal maps
• Conformal graph directed Markov systems
• Examples of GDMS in Carnot groups
• Countable alphabet symbolic dynamics : foundations of the thermodynamic formalism
• Hausdorff dimension of limit sets
• Conformal measures and regularity of domains
• Examples revisited
• Finer properties of limit sets : Hausdorff, packing and invariant measures
• Equivalent separation conditions for finite GDMS

The authors develop a comprehensive theory of conformal graph directed Markov systems in the non-Riemannian setting of Carnot groups equipped with a sub-Riemannian metric. In particular, they develop the thermodynamic formalism and show that, under natural hypotheses, the limit set of an Carnot conformal GDMS has Hausdorff dimension given by Bowen's parameter. They illustrate their results for a variety of examples of both linear and nonlinear iterated function systems and graph directed Markov systems in such sub-Riemannian spaces. These include the Heisenberg continued fractions introduced by Lukyanenko and Vandehey as well as Kleinian and Schottky groups associated to the non-real classical rank one hyperbolic spaces.
(source: Nielsen Book Data)

• Foundations of conservation biology
• Importance of biodiversity
• Threats to biodiversity
• Approaches to conservation

"Brings together theory, applied research, basic research, and hundreds of real-world examples and stories from dozens of disciplines to teach students how to be practicing conservation biologists that protect and manage Earth's biodiversity while sustaining a high quality of life for humankind." -- Back cover

• Simple quadrilaterals
• Quadrilaterals and their circles
• Diagonals of quadrilaterals
• Properties of trapezoids
• Applications of trapezoids
• Garfield trapezoids and rectangles
• Parallelograms
• Rectangles
• Squares
• Special quadrilaterals
• Quadrilateral numbers.

"A Cornucopia of Quadrilaterals collects and organizes hundreds of beautiful and surprising results about four-sided figures--for example, that the midpoints of the sides of any quadrilateral are the vertices of a parallelogram, or that in a convex quadrilateral (not a parallelogram) the line through the midpoints of the diagonals (the Newton line) is equidistant from opposite vertices, or that, if your quadrilateral has an inscribed circle, its center lies on the Newton line. There are results dating back to Euclid: the side-lengths of a pentagon, a hexagon, and a decagon inscribed in a circle can be assembled into a right triangle (the proof uses a quadrilateral and circumscribing circle); and results dating to Erdős: from any point in a triangle the sum of the distances to the vertices is at least twice as large as the sum of the distances to the sides. The book is suitable for serious study, but it equally rewards the reader who dips in randomly. It contains hundreds of challenging four-sided problems. Instructors of number theory, combinatorics, analysis, and geometry will find examples and problems to enrich their courses. The authors have carefully and skillfully organized the presentation into a variety of themes so the chapters flow seamlessly in a coherent narrative journey through the landscape of quadrilaterals. The authors' exposition is beautifully clear and compelling and is accessible to anyone with a high school background in geometry"-- Provided by publisher.

For two-semester courses in astronomy. Exploring the impact of new discoveries on astronomy, science, and life in the universe Building on a long tradition of effective pedagogy and comprehensive coverage, The Cosmic Perspective, 9th Edition provides a thoroughly engaging and up-to-date introduction to astronomy for anyone who is curious about the universe, regardless of prior background in astronomy or physics. As respected teachers and active researchers, the authors present astronomy using a coherent narrative and a thematic approach that engages students immediately and guides them through connecting ideas. This engagement-centered approach and variety of contextualizing features enhance student understanding of the process of science and actively involve them in learning key concepts. The 9th Edition features major scientific updates, new content that focuses on the possibility of life in the universe, and recent discoveries that provide modern contexts to help students see astronomy as highly relevant to their worlds now. The authors integrate a new focus on cultural diversity among scientists and ethics across science and astronomy, delving into science done by a wide range of people and evaluated in different ways. The authors write and create a wealth of Mastering Astronomy resources, carrying the coherent and cohesive approach of the book to the new and expanded digital tools, such as Prelecture Videos. Instructors can access this curated group of activities in Mastering Astronomy for use before, during, and after class and can easily edit the pre-built assignments to fit the way they teach. This text is also available in two volumes, which can be purchased separately: The Cosmic Perspective: The Solar System, 9th Edition (includes Chapters 1-13, 14, S1, 24) The Cosmic Perspective: Stars, Galaxies, and Cosmology, 9th Edition (includes Chapters 1-3, S1, 4-6, S2-S4, 14-24) Also available digitally as a standalone Pearson eText, or via Mastering Astronomy, which includes the Pearson eText. Pearson eText is a simple-to-use, mobile-optimized, personalized reading experience that can be adopted on its own as the main course material. It lets students highlight, take notes, and review key vocabulary all in one place, even when offline. Seamlessly integrated videos and other rich media engage students and give them access to the help they need, when they need it. Educators can easily customize the table of contents and share their own notes with students so they see the connection between their eText and what they learn in class - motivating them to keep reading, and keep learning. If your instructor has assigned Pearson eText as your main course material, search for: - 0135729491 / 9780135729496 Pearson eText Cosmic Perspective, The -- Access Card, 9/e OR - 0135729459 / 9780135729458 Pearson eText Cosmic Perspective, The -- Instant Access, 9/e Also available with Mastering Astronomy By combining trusted author content with digital tools and a flexible platform, Mastering personalizes the learning experience and improves results for each student.Resources in Mastering Astronomy are written and carefully reviewed by the author team, establishing the same coherent and trusted voice as the book. Note: You are purchasing a standalone product; Mastering Astronomy does not come packaged with this content. Students, if interested in purchasing this title with Mastering Astronomy, ask your instructor for the correct package ISBN and Course ID. Instructors, contact your Pearson representative for more information. If you would like to purchase both the physical text and Mastering Astronomy, search for: 0134988930 / 9780134988931 Cosmic Perspective, The Plus Mastering Astronomy with Pearson eText -- Access Card Package Package consists of: 0134874366 / 9780134874364 Cosmic Perspective, The 0134988833 / 9780134988832 Mastering Astronomy with Pearson eText -- ValuePack Access Card -- for Cosmic Perspective, The 0321765184 / 9780321765185 SkyGazer 5.0 Student Access Code Card (Integrated component).
(source: Nielsen Book Data)

"Embryologist Magdalena Zernicka-Goetz has spent two decades unraveling the mysteries of fetal development. By studying embryonic mouse cells, she witnessed the embryo's ability to rid itself of abnormal cells as it prepared for implantation in the womb. When Zernicka-Goetz became pregnant at 44, she received a call that took her by surprise: a sample test of the cells in her own placenta indicated that the fetus had trisomy-2, a disastrous extra copy of the second chromosome, which increased the risk of miscarriage or serious birth defects. It seemed likely that the best choice was to have an abortion. But the plasticity of the embryonic mouse cells in her studies gave her hope; if mouse cells were able to course correct, then perhaps human cells were capable of similar resiliency. Six months later, she gave birth to a healthy baby boy, and the experience inspired her to begin a series of studies to test this hypothesis. Her subsequent experiments with early human embryos and artificial "three parent" embryos were not only groundbreaking; they also proved that embryotic cells could be artificially nurtured through the trials and tribulations of their early development. To say that her work is controversial would be an understatement, but as Zernicka-Goetz notes, harm can arise as much from doing nothing as from taking risks. And with profound implications for stem cell research, infertility treatment, prenatal diagnostic testing, immunotherapy, and genetic engineering, not to mention women's reproductive health, the stakes have never been higher. At once thought-provoking and thoroughly moving, The Dance of Life sheds new light on how a simple fertilized egg becomes a complex human being"-- Provided by publisher

• Introduction. Dessins d'enfants: From polynomials through Belyi functions to weighted trees. Existence theorem. Recapitulation and perspective. Classification of unitrees. Computation of Davenport-Zannier pairs for unitrees. Primitive monodromy groups of weighted trees. Trees with primitive monodromy groups. A zoo of examples and constructions. Diophantine invariants. Enumeration. What remains to be done. Bibliography. Index.
• (source: Nielsen Book Data)

The French expression "dessins d'enfants'' means children's drawings. This term was coined by the great French mathematician Alexandre Grothendieck in order to denominate a method of pictorial representation of some highly interesting classes of polynomials and rational functions. The polynomials studied in this book take their origin in number theory. The authors show how, by drawing simple pictures, one can prove some long-standing conjectures and formulate new ones. The theory presented here touches upon many different fields of mathematics. The major part of the book is quite elementary and is easily accessible to an undergraduate student. The less elementary parts, such as Galois theory or group representations and their characters, would need a more profound knowledge of mathematics. The reader may either take the basic facts of these theories for granted or use our book as a motivation and a first approach to these subjects.
(source: Nielsen Book Data)

• 1 Regularity in several variables.- 1 Geometric models of divisorially valued function fields.- 2 Logarithmic differential operators.- 3 Connections regular along a divisor.- 4 Extensions with logarithmic poles.- 5 Regular connections: the global case.- 6 Exponents.- Appendix A: A letter of Ph. Robba (Nov. 2, 1984).- Appendix B: Models and log schemes.- 2 Irregularity in several variables.- 1 Spectral norms.- 2 The generalized Poincare-Katz rank of irregularity.- 3 Some consequences of the Turrittin-Levelt-Hukuhara theorem.- 4 Newton polygons.- 5 Stratification of the singular locus by Newton polygons.- 6 Formal decomposition of an integrable connection at a singular divisor.- 7 Cyclic vectors, indicial polynomials and tubular neighborhoods.- 3 Direct images (the Gauss-Manin connection).- 1 Elementary fibrations.- 2 Review of connections and De Rham cohomology.- 3 Devissage.- 4 Generic finiteness of direct images.- 5 Generic base change for direct images.- 6 Coherence of the cokernel of a regular connection.- 7 Regularity and exponents of the cokernel of a regular connection.- 8 Proof of the main theorems: finiteness, regularity, monodromy, base change (in the regular case).- Appendix C: Berthelot's comparison theorem on OXDX-linear duals.- Appendix D: Introduction to Dwork's algebraic dual theory.- 4 Complex and p-adic comparison theorems.- 1 Review of analytic connections and De Rham cohomology.- 2 Abstract comparison criteria.- 3 Comparison theorem for algebraic vs.complex-analytic cohomology.- 4 Comparison theorem for algebraic vs. rigid-analytic cohomology (regular coefficients).- 5 Rigid-analytic comparison theorem in relative dimension one.- 6 Comparison theorem for algebraic vs. rigid-analytic cohomology (irregular coefficients).- 7 The relative non-archimedean Turrittin theorem.- Appendix E: Riemann's "existence theorem" in higher dimension, an elementary approach.- References.
• (source: Nielsen Book Data)

"...A nice feature of the book [is] that at various points the authors provide examples, or rather counterexamples, that clearly show what can go wrong...This is a nicely-written book [that] studies algebraic differential modules in several variables." --Mathematical Reviews.
(source: Nielsen Book Data)

• Degree theory
• Applications

The authors develop a degree theory for compact immersed hypersurfaces of prescribed $K$-curvature immersed in a compact, orientable Riemannian manifold, where $K$ is any elliptic curvature function. They apply this theory to count the (algebraic) number of immersed hyperspheres in various cases: where $K$ is mean curvature, extrinsic curvature and special Lagrangian curvature and show that in all these cases, this number is equal to $-\chi(M)$, where $\chi(M)$ is the Euler characteristic of the ambient manifold $M$.
(source: Nielsen Book Data)